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<p>Works by Humberstone (1981, 2011), van Benthem (1981, 2016), Holliday (2014, 2025), and Ding and Holliday (2020) develop a semantics of modal logic in terms of “possibilities”, i.e., “less determinate entities than possible worlds” (Edgington, 1985). These works take possibilities as semantically primitive entities, stipulate a number of semantic principles that govern these entities (Ordering, Persistence, Refinement, Cofinality, Negation, and Conjunction), and then interpret a modal language via this semantic structure. In this paper, we <i>define</i> possibilities in object theory (OT), and <i>derive</i>, as theorems, the semantic principles stipulated in the works cited. We then derive a fundamental theorem that shows our theory of possibilities is correct: we prove that the possibilities we’ve defined correspond one-to-one with the true possibility claims of the object language. By contrast, the possibility semanticist has to stipulate this correspondence in the semantic clause providing truth conditions of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\scalebox{0.7}[0.7]{$\Diamond$}} \varphi\)</EquationSource> </InlineEquation>.</p>

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The metaphysics of possibility semantics

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Uri Nodelman,
  • Edward N. Zalta

摘要

Works by Humberstone (1981, 2011), van Benthem (1981, 2016), Holliday (2014, 2025), and Ding and Holliday (2020) develop a semantics of modal logic in terms of “possibilities”, i.e., “less determinate entities than possible worlds” (Edgington, 1985). These works take possibilities as semantically primitive entities, stipulate a number of semantic principles that govern these entities (Ordering, Persistence, Refinement, Cofinality, Negation, and Conjunction), and then interpret a modal language via this semantic structure. In this paper, we define possibilities in object theory (OT), and derive, as theorems, the semantic principles stipulated in the works cited. We then derive a fundamental theorem that shows our theory of possibilities is correct: we prove that the possibilities we’ve defined correspond one-to-one with the true possibility claims of the object language. By contrast, the possibility semanticist has to stipulate this correspondence in the semantic clause providing truth conditions of \({\scalebox{0.7}[0.7]{$\Diamond$}} \varphi\) .